Pith Number

pith:66EUA4RJ

pith:2025:66EUA4RJSQMUN35IEEPUHGVTPF

not attested not anchored not stored refs pending

Sum-product phenomena for Ahlfors-regular sets

William O'Regan

arxiv:2501.02131 v3 · 2025-01-03 · math.CA · math.CO · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{66EUA4RJSQMUN35IEEPUHGVTPF}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T11:45:55.039046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f789407229941946efa8211f439ab3796528539df2ce541dbf7c60ea4b8c7ef2

Aliases

arxiv: 2501.02131 · arxiv_version: 2501.02131v3 · doi: 10.48550/arxiv.2501.02131 · pith_short_12: 66EUA4RJSQMU · pith_short_16: 66EUA4RJSQMUN35I · pith_short_8: 66EUA4RJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/66EUA4RJSQMUN35IEEPUHGVTPF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f789407229941946efa8211f439ab3796528539df2ce541dbf7c60ea4b8c7ef2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "623d1ed0f5c2d9cb678b520b0fe0f4beae7190ac2501de4a3194bb439d840ea4",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-01-03T22:51:02Z",
    "title_canon_sha256": "b74e3bfedf90d8a207991f296bcf2e2f623a127a7678eb2e015f2860844740e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.02131",
    "kind": "arxiv",
    "version": 3
  }
}